If \( \cot x = \dfrac{5}{12} \) for some \( x \in \left({\pi}, \dfrac{3\pi}{2}\right) \), then \( \sin 7x \left( \cos \dfrac{13x}{2} + \sin \dfrac{13x}{2} \right) + \cos 7x \left( \cos \dfrac{13x}{2} - \sin \dfrac{13x}{2} \right) \) is equal to:
\( \dfrac{5}{\sqrt{13}} \)
\( \dfrac{1}{\sqrt{13}} \)
\( \dfrac{6}{\sqrt{26}} \)
\( \dfrac{4}{\sqrt{26}} \)
